Phylogenetic networks have been introduced as a model generalizing phylogenetic trees in order to represent the evolution of species. Contrary to trees, it allows to represent the transfer of genetic material between coexisting species or populations, through recombination, hybridization or horizontal gene transfers. Several methods have been proposed to reconstruct phylogenetic networks by combining together gene trees, where each gene tree represents the evolution of one gene. These methods expect the gene trees to be contained in the reconstructed phylogenetic network, but given the tree and the network, just checking if the tree is contained in the network is already an NP-hard problem. We will present some subclasses of phylogenetic networks where polynomial-time algorithms can be found for this decision problem, as well as a system describing those subclasses and their inclusions.